Modularity of formal Fourier--Jacobi series from a cohomological point of view
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908142104739840 |
|---|---|
| author | Flores, Marco |
| author_facet | Flores, Marco |
| contents | We investigate the modularity of formal Fourier--Jacobi series by establishing cohomological vanishing results for line bundles defined on compactifications of $\mathcal{A}_g$. Working over $\mathbb{C}$, we show that the minimal compactification of $\mathcal{A}_2$ has only rational singularities, which allows us to characterize, for sufficiently large weights, the modularity of formal Fourier--Jacobi series of genus~$2$ via cohomological vanishing. Working over $\mathbb{Z}$, we introduce a level $n\geq 3$ structure and, via the the resolution morphism from a toroidal compactification of $\mathcal{A}_{g,n}$ to its minimal compactification, we characterize the modularity of arithmetic formal Fourier--Jacobi series with a level $n\geq 3$ structure and sufficiently large weight via cohomological vanishing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_12691 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Modularity of formal Fourier--Jacobi series from a cohomological point of view Flores, Marco Algebraic Geometry Number Theory We investigate the modularity of formal Fourier--Jacobi series by establishing cohomological vanishing results for line bundles defined on compactifications of $\mathcal{A}_g$. Working over $\mathbb{C}$, we show that the minimal compactification of $\mathcal{A}_2$ has only rational singularities, which allows us to characterize, for sufficiently large weights, the modularity of formal Fourier--Jacobi series of genus~$2$ via cohomological vanishing. Working over $\mathbb{Z}$, we introduce a level $n\geq 3$ structure and, via the the resolution morphism from a toroidal compactification of $\mathcal{A}_{g,n}$ to its minimal compactification, we characterize the modularity of arithmetic formal Fourier--Jacobi series with a level $n\geq 3$ structure and sufficiently large weight via cohomological vanishing. |
| title | Modularity of formal Fourier--Jacobi series from a cohomological point of view |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2411.12691 |